This study is designed to investigate the safety and tolerability of a new drug, AZD5363, in patients with advanced cancer - and to identify a dose and schedule that can be used in the future. This study will also investigate how the body handles AZD5363 (ie, how quickly the body absorbs and removes the drug). This study will also investigate anti-tumour activity of AZD5363 in patients with advanced / metastatic breast, gynaecological cancers or other solid cancers bearing either AKT1 / PIK3CA or PTEN mutation.